As a portfolio manager, you manage 10,000 units (each unit is equal to $100) of the Treasury portfolio with 5-year maturity with a money duration of 399. In March 2022, the RBA (Reserve Bank of Australia) cash rate was 0.1%, and there had been market rumors that RBA would raise the interest rate in 2022. There are 3-year (money duration 215) and 8-year (money duration 652) Treasury bonds in the market. You plan to take a hedge position to avoid the negative impact on your portfolio valuation.

Question:

(a) How do you set up a butterfly portfolio that can theoretically isolate your portfolio from an interest rate hike? Please calculate the positions of your hedge portfolio. You should construct the hedging portfolio with money neutral and money duration neutral.

(b) What is the pattern of the theoretical returns of the butterfly hedging strategy if the interest rate hikes are at different levels of 20 bps, 30bps, 40bps, or 50 bps?

(c) What is the risk of the butterfly hedging strategy?